TY - JOUR
AB - We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N
Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).
AU - Cipolloni, Giorgio
AU - Erdös, László
AU - Schröder, Dominik J
ID - 11418
IS - 3
JF - Annals of Probability
SN - 0091-1798
TI - Normal fluctuation in quantum ergodicity for Wigner matrices
VL - 50
ER -